Monodromy Approach to the Scaling Limits in Isomonodromy Systems

The isomonodromy deformation method is applied to the scaling limits in the linear $(N\times N)$ matrix equations with rational coefficients to obtain the deformation equations for the algebraic curves that describe the local behavior of the reduced versions for the relevant isomonodromy deformation equations. The approach is illustrated by the study of the algebraic curve associated with the $n$-large asymptotics in the sequence of the biorthogonal polynomials with cubic potentials.